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The Common Core State Standards for Mathematics. Transitioning to the Common Core. K-8 Content Standards. Grade. Domain. Cluster. Standard. K-8 Grade Level Overview. Critical Areas – similar to NCTM’s Curriculum Focal Points. Grade Level. Format of K-8 Standards. Domain. Cluster. - PowerPoint PPT Presentation
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The Common Core State Standards for Mathematics
Transitioning to the Common Core
K-8 Content StandardsK-8 Content StandardsGrade
Domain
Cluster
Standard
K-8 Grade Level Overview
Critical Areas Critical Areas – similar to – similar to
NCTM’s NCTM’s Curriculum Curriculum Focal PointsFocal Points
Format of K-8 Standards Grade Grade LevelLevel
DomainDomain
Format of K-8 Standards
ClusterCluster
ClusterCluster
StandardStandard
StandardStandard
Domain K 1 2 3 4 5Counting and Cardinality (CC)
Operations and Algebraic Thinking (OA)
Number and Operations in Base Ten (NBT)
Measurement and Data (MD)
Geometry (G)
Numbers and Operations- Fractions (NF)
DomainsDomains
Domain 6 7 8
Ratios and Proportional Relationships (RP)
The Number System (NS)
Expressions and Equations (EE)
Geometry (G)
Statistics and Probability (SP)
Functions (F)
DomainsDomains
High School Conceptual Categories
• The big ideas that connect mathematics across high school – such as Functions or Probability and Statistics
• A progression of increasing complexity• Description of mathematical content to be
learned elaborated through domains, clusters, and standards
• Number and Quantity • Algebra • Functions • Geometry • Statistics and Probability • Modeling
High School Conceptual Categories
Pathways
• Four model pathways:– Traditional Pathway (Algebra 1, Geometry,
Algebra 2)– Integrated Pathway– Compacted Traditional Pathway*– Compacted Integrated Pathway*
*7th, 8th, and Algebra 1 standards covered in 2 years
See CCSSM APPENDIX A for course descriptions for both pathways.
8 CCSS Mathematical Practices1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
SMARTER Balanced Assessment Consortium System Highlights
Assessment Design
The Consortium will provide the following by the 2014-15 school year:
3. Formative tools and resources4. Responsible flexibility5. Distributed summative assessment
a. Content clusters throughout a courseb. Most appropriate time for each studentc. Scores rolled up
Smarter Balanced Assessment Consortium
Link to Practice StandardsFour Claims Used in Draft 2 Test Specifications
Claim 1 ≈ 40% of assessmentClaim 2 ≈ 20% of assessmentClaim 3 ≈ 20% of assessmentClaim 4 ≈ 20% of assessment
SHIFT #1: Focus
Similar to the Oregon standards in Mathematics, the intent of the CCSSM is to narrowly and deeply focus the time and energy spent in the math classroom.
The CCSSM emphasizes concepts prioritized in the
standards so that students reach strong foundational knowledge and deep conceptual understanding and are able to transfer mathematical skills and understanding across concepts and grades.
The Three-Legged Stool
In order to focus on content, you must teach to address all three legs of mathematical learning:• Conceptual
Understanding• Computational Fluency• Problem-Solving
Draft Emphases (Sample – Grade 6)Ratios and Proportional Relationships[m] Understand ratio concepts and use ratio reasoning to solve problems.
The Number System[m] Apply and extend previous understandings of multiplication and division to divide fractions by fractions.[a] Compute fluently with multi-digit numbers and find common factors and multiples.[m] Apply and extend previous understandings of numbers to the system of rational numbers.
Expressions and Equations[m] Apply and extend previous understandings of arithmetic to algebraic expressions.[m] Reason about and solve one-variable equations and inequalities.[m] Represent and analyze quantitative relationships between dependent and independent variables
Geometry[s] Solve real-world and mathematical problems involving area, surface area, and volume.
Statistics and Probability[a] Develop understanding of statistical variability.[a] Summarize and describe distributions.
Activity: Focus (find a partner or small group at your grade level)
Grades K-2• Read through the
Critical Areas page of your standards
• Discuss with a partner how you could better address all three legs of the “mathematics” stool in these areas
Grades 3-HS• Pick up the appropriate
Emphases page from the front
• Look at the “m” clusters and discuss how you could better address all three legs of the “mathematics” stool in these areas
Deep conceptual understanding of core content at each grade is critical for student success in subsequent years.
Each standard is not a new event, but an
extension of previous learning. For example, fractions and multiplication build across grade levels and students can scaffold new understanding onto foundations built in previous years.
SHIFT #2: Coherence
Activity: Coherence(with same partner or small group at your grade level)
Grades K-2• Look at the standards not
in your critical areas (may fall in the same domain but be listed at the end)
• How are these connecting to your grade level while introducing or reinforcing other grade level skills?
Grades 3-8• Look at the “s” and “a”
clusters. How are these connecting to your grade level while introducing or reinforcing other grade level skills?
Activity: Coherence (Cont)(with same partner or small group at your grade level)
High School• Only your major emphases are listed on the Emphases
handout. • Coherence may come from connecting and reinforcing
previous grade level standards. • How do the additional and supporting (non-major)
standards fit into your program(s)?
Shift #4: Modeling Modeling links classroom mathematics and statistics to
everyday life, work, and decision-making– Choose and use appropriate mathematics to analyze situations– Better understanding real-world scenarios involving math
Teachers at all grade levels should identify
opportunities for students to apply math concepts
in “real world” situations.
Activity: Modeling
1. Locate your goldenrod stations activity template.
2. Visit between 4-6 stations.Pink Cards = Elementary ContentBlue Cards = Middle/High School Content
3.While visiting stations, have others sign off on the correctness of your answer. Nobody can sign your paper
more than twice.
4. When finished, return to your seat and answer the two questions at the bottom of the page.
Performance TaskChoose a new partner or small group:
Elementary or Secondary
1. Pick up the appropriate performance task up front.
Options: Elementary (4th Grade) or High School
2. Understand purpose and placement of task in classroom instruction and assessment.
3. Read/Attempt the task.
4. Discuss implications for classroom instruction.
Contact Information
Shannon McCaw, SMc Curriculumwww.SMcCurriculum.com